Qualitative counting closed geodesics

Bastien Karlhofer, Jarek Kędra* (Corresponding Author), Michał Marcinkowski, Alexander Trost

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We investigate the geometry of word metrics on fundamental groups of manifolds associated with the generating sets consisting of elements represented by closed geodesics. We ask whether the diameter of such a metric is finite or infinite. The first answer we interpret as an abundance of closed geodesics, while the second one as their scarcity. We discuss examples for both cases.
Original languageEnglish
Pages (from-to)523-530
JournalGeometriae Dedicata
Early online date28 Jan 2021
Publication statusPublished - 31 Aug 2021


  • math.DG
  • math.GR
  • math.GT


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